Nonequilibrium dynamics of the $σ$-model modes on the de Sitter space
The two-dimensional $σ$-model with the de Sitter target space has a local canonical description in the north pole diamond of the Penrose diagram in the cosmological gauge. The left and right moving modes on the embedded base space with the topology of a cylinder are entangled among themselves and in...
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ftdatacite:10.48550/arxiv.1701.05582 2023-05-15T17:39:58+02:00 Nonequilibrium dynamics of the $σ$-model modes on the de Sitter space Vancea, Ion V. 2017 https://dx.doi.org/10.48550/arxiv.1701.05582 https://arxiv.org/abs/1701.05582 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ High Energy Physics - Theory hep-th FOS Physical sciences Preprint Article article CreativeWork 2017 ftdatacite https://doi.org/10.48550/arxiv.1701.05582 2022-04-01T10:46:45Z The two-dimensional $σ$-model with the de Sitter target space has a local canonical description in the north pole diamond of the Penrose diagram in the cosmological gauge. The left and right moving modes on the embedded base space with the topology of a cylinder are entangled among themselves and interact with the time-dependent components of the metric of the de Sitter space. Firstly we address the issue of the existence of the untangled oscillator representation and the description of the nonequilibrium dynamics of the untangled modes. We show that the untangled oscillators can be obtained from the entangled operators by applying a set of Bogoliubov transformations that satisfy a set of constraints that result from the requirement that the partial evolution generator be diagonal. Secondly, we determine the nonequilibrium dynamics of the untangled modes in the Non-Equilibrium Thermo Field Dynamics formalism. In this setting, the thermal modes are represented as thermal doublet oscillators that satisfy partial evolution equations of Heisenberg-type. We use these equations to compute the local free one-body propagator of an arbitrary mode between two times. Thirdly, we discuss the field representation of the thermal modes. We show that there is a set of thermal doublet fields that satisfy the equal time canonical commutation relations, are solutions to the $σ$-model equations of motion and can be decomposed in terms of thermal doublet oscillators. Finally, we construct a local partial evolution functional of Hamilton-like form for the thermal doublet fields. : 21 pages Report North Pole DataCite Metadata Store (German National Library of Science and Technology) North Pole Sitter ENVELOPE(10.986,10.986,64.529,64.529) |
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DataCite Metadata Store (German National Library of Science and Technology) |
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unknown |
topic |
High Energy Physics - Theory hep-th FOS Physical sciences |
spellingShingle |
High Energy Physics - Theory hep-th FOS Physical sciences Vancea, Ion V. Nonequilibrium dynamics of the $σ$-model modes on the de Sitter space |
topic_facet |
High Energy Physics - Theory hep-th FOS Physical sciences |
description |
The two-dimensional $σ$-model with the de Sitter target space has a local canonical description in the north pole diamond of the Penrose diagram in the cosmological gauge. The left and right moving modes on the embedded base space with the topology of a cylinder are entangled among themselves and interact with the time-dependent components of the metric of the de Sitter space. Firstly we address the issue of the existence of the untangled oscillator representation and the description of the nonequilibrium dynamics of the untangled modes. We show that the untangled oscillators can be obtained from the entangled operators by applying a set of Bogoliubov transformations that satisfy a set of constraints that result from the requirement that the partial evolution generator be diagonal. Secondly, we determine the nonequilibrium dynamics of the untangled modes in the Non-Equilibrium Thermo Field Dynamics formalism. In this setting, the thermal modes are represented as thermal doublet oscillators that satisfy partial evolution equations of Heisenberg-type. We use these equations to compute the local free one-body propagator of an arbitrary mode between two times. Thirdly, we discuss the field representation of the thermal modes. We show that there is a set of thermal doublet fields that satisfy the equal time canonical commutation relations, are solutions to the $σ$-model equations of motion and can be decomposed in terms of thermal doublet oscillators. Finally, we construct a local partial evolution functional of Hamilton-like form for the thermal doublet fields. : 21 pages |
format |
Report |
author |
Vancea, Ion V. |
author_facet |
Vancea, Ion V. |
author_sort |
Vancea, Ion V. |
title |
Nonequilibrium dynamics of the $σ$-model modes on the de Sitter space |
title_short |
Nonequilibrium dynamics of the $σ$-model modes on the de Sitter space |
title_full |
Nonequilibrium dynamics of the $σ$-model modes on the de Sitter space |
title_fullStr |
Nonequilibrium dynamics of the $σ$-model modes on the de Sitter space |
title_full_unstemmed |
Nonequilibrium dynamics of the $σ$-model modes on the de Sitter space |
title_sort |
nonequilibrium dynamics of the $σ$-model modes on the de sitter space |
publisher |
arXiv |
publishDate |
2017 |
url |
https://dx.doi.org/10.48550/arxiv.1701.05582 https://arxiv.org/abs/1701.05582 |
long_lat |
ENVELOPE(10.986,10.986,64.529,64.529) |
geographic |
North Pole Sitter |
geographic_facet |
North Pole Sitter |
genre |
North Pole |
genre_facet |
North Pole |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1701.05582 |
_version_ |
1766140723913031680 |